The Naib has requested I put out a few more posts, particularly of the mathematical variety. I finished my math degree two years ago, so it actually is pretty fun for me to think about it now (although, I must admit, the classes got painful sometimes).
Anyway, I really like the Naib and am quite willing to accomodate him, so here is another one since I seem to be in a posting mood today.
Did you know that no one had ever been able to prove that the premises behind Eucidean Geometry (you know, where all triangles have 180 degrees-the geometry you did in high school, if you took geometry) were always true?
Turns out, you can have several types of geometry: Eucidean; the kind where you assume triangles have over 180 degrees; and the kind where you assume triangles have under 180 degrees.
As it turns out, one of the last two has been very useful in attempting to figure out how galaxies, black holes and the like work but for the ordinary Earth sized stuff, it is best to work with the assume a triangle has 180 degrees.
Maybe you knew that, maybe you didn’t. I, personally, found it to be fascinating.
I came across this reading Mr Tompkins In Paperback (if you are interested in relativity but don’t understand it then this is the book for you). Basically the non-Euclidian geometry comes about when trying to carry out mathematical operations in an environment that has different characteristics than those for which the operations were created.
A triangle has internal angles exceeding 180 degrees when projected onto a convex surface, and less than 180 degrees on a concave surface. I’m not sure what would happen if this was projected onto a four dimensional surface – all sorts of fun, I would guess – but it does say something important about our shallow understanding of the world about us.
How many people, for instance, know that pumping your car tyres up from a less than perfect state can save 10% on vehicle emissions. Give people information and they might use it.
BTW : Non-Euclidean geometry allow airlines to use the shortest distances across the globe – not that I would ever fly…